In a meeting, 70% of the members favour and 30% oppose a certain proposal. A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour. Find E(X) and Var (X).

In class XI of a school 40% of the students study Mathematics and 30% study Biology. 10% of the class study both mathematics and biology. If a student is selected at random from the class, find the probability that he will be studying Mathematics or Biology or both.

In Class XI of a school 40% of the students study Mathematics and 30% study Biology. 10% of the class study both Mathematics and Biology. If a student is selected at random from the class, find the probability that he will be studying Mathematics or Biology.

Let a pair of dice he rolled thrice and the random variable X be the number of doublets. Find the mean of the random variable.

The members of a consulting firm rent cars from three agencies: 50% from agency X, 30% from agency Y and rest from agency Z. From past experience it is known that 9% of the cars from agency X need a service and tuning before renting, 12% of the cars from agency Y need a service and tuning before renting and 10% of the cars from agency Z need a service and tuning before renting. If the rental car delivered to the firm needs service and tuning, find the probability that agency Z is not to be blamed.

In a class, 30% students study English, 15% study Hindi and 10% study both English and Hindi. One student is selected at random. Find the probability that (i) He studies English if it known that he Hindi (ii) He studies Hindi if it is known that he studies English

Find the approximate percentage increase in volume of a cube of side x metre if the percentage increase in its side is 1%.

If f'(x)=x e^(x) and f(0)=1 then find f(x).

Find the area of the region bounded by y=e^(x) and y = x between x = 0 and x = 1.

The random variable X can take only the values 0, 1, 2. Given that P(X=0) = P(X= 1) = p and E(X^2) = E(X) , then find the value of p